Journal of Applied & Computational Mathematics

Kumar M

Publications

• Research Article
  Cryptographic Schemes Based on Elliptic Curves over the Ring Zp[i]
  Author(s): Kumar M and Gupta PKumar M and Gupta P
  
  Elliptic Curve Cryptography recently gained a lot of attention in industry. The principal attraction of ECC compared to RSA is that it offers equal security for a smaller key size. The present paper includes the study of two elliptic curve Ea,b and Ea,-b defined over the ring Zp[i] where i2 = -1. After showing isomorphism between Ea,b and Ea,-b. We define a composition operation (in the form of a mapping) on their union set. Then we have discussed our proposed cryptographic schemes based on the elliptic curve E = Ea,b∪Ea,-b. We also illustrate the coding of points over E, secret key exchange and encryption/decryption methods based on above said elliptic curve. Since our proposed scheme are based on elliptic curve of the particular type therefore the proposed schemes provides a highest strength-per-bit of any cryptosystem known today with smaller key size resulting in faster comput.. Read More»
  DOI: 10.4172/2168-9679.1000288

  Abstract PDF